The computer SONY VAIO PCG-5K1L knows more than half a century, rapid development has attracted a reflection of the extreme fertility. This has led to use the existing mathematical theories, which are then enriched (arithmetic, graph theory, information theory), or new areas of mathematics (eg, complexity theory to the theory of computation) to create. A new mathematical sensitivity resulting from the use of computers Sony VGP-BPS9/B and the problems they pose for the theory of mind. If all of 1930 with the work of the Austrian Kurt Godel, Alan Turing and the British in the American church Alonso on the concept of mathematical algorithm, this new awareness has developed in recent decades. In addition to continuous mathematics, discrete mathematics and computer information in full bloom, and it is very far from the race, although the main corridors.
Organize billion calculations?
Give commands to some computers Sony VGP-BPS22, what is expected of them "to write programs." Mathematicians have always hold such methods of calculation, but in practical work, the implicit rule that were in the algorithms used in the hands of a few tens or hundreds of elementary operations. If the machines can be millions or billions of calculations to no error was available, it was discovered that a new science, algorithms, and the development of this science was essentially mathematical summer. Automatic control of computers SONY VGP-BPS13B/Q Battery is neither simple nor obvious, and prove satisfactory methods at first, no sense in the world of computing. Solve linear equations with Gabriel Cramer, Swiss formula (which reports express the determinants of solutions) is not with the systems of size 30 is concerned, while other methods go far beyond. Computers of all kinds, collide with the limits, and that's before the hand that writes programs and never think to say that the performance of the machine to compensate for the lack of preliminary analysis.
The real rule is a more powerful machine to produce the early work in mathematics, so they work properly and check the operation.
A problem as simple as the multiplication of integers leads to the development of complex and sensitive methods when it comes to manipulating numbers in large sizes with thousands, millions or even billions of numbers. We were surprised to see that in a case like the basic course was possible. But in 1970, Sony VGP-BPS2 Battery has developed methods for multiplying two n-digit time proportional to n × ln (n) x ln (ln (n)). In practice this is almost synonymous with a time proportional to n, and realized much faster than traditional methods of procedure by hand, thousands of years, which in turn require a working time proportional to N2 and N3. What can you with the contemporary law of the multiplication algorithm is not without it, and rely solely on Moore's Law (which is a doubling of computing power every 18 months) should be 2050 or more to get there.
Incredible progress
This algorithm can be revised, completed and perfected, and the progress in electronics, there is progress in the calculation of mathematical constants and were just getting billions of decimals of the most important of them. .. These HP Pavilion DV7 Series advances have sometimes surprises like the discovery of a Canadian team in 1995, a new formula and a method to support this formula, which gives the number of binary used independently.
This theoretical result was in practice by Colin Percival, who in September 2000, she received a piece of binary digits in the 1015 th binary digit converted. This performance seemed out of reach for many centuries. This is a good algorithm to do without them.
Other consequences of this control algorithm arithmetic, with a large number, we have already mentioned, the discovery of the first record: a prime number of two million jobs in 1999 and recently completed a series of more than 10 million digits. Again, the discovery of the probabilistic primality Lenovo G560 Battery test (which is not an absolute certainty, but with a small risk of error, an integer, the first) a theory of Surprise also very useful in cryptography.
Beyond the computer used, sometimes anecdotal, the entire science of the organization of the calculations, matures and progresses, creating a deep connection with mathematics and sometimes radically changed the view. Arithmetic books of a new genre has emerged in which the concepts introduced systematically associated with algorithmic tools to effectively use a computer Toshiba Satellite M305 Series. Mathematics is needed to control computers and help them understand in depth, but in return the computer to do math in a different way to practice and give a new vision of abstract objects that the car is better than the human mind and with greater security.
Closer links
It is not just arithmetic, but an important part of mathematics that deals with the progress of the algorithm. Computer Algebra (calculated with the computer not only numbers but also symbols, functions, equations, etc.). It has increased considerably. However, the relationship between computer Toshiba Satellite M305D-S4844 science and math is not everything. Note:
numerical analysis, which solves large systems of equations;
mathematical logic and its extensions, used in artificial intelligence in databases for the development of automated deduction methods and certification programs;
Modeling and simulation, and graphics using a variety of discrete structures allow the reproduction of objects and complex systems in physics, economics and biology;
Computer security and encryption, a new set of problems that often creates the context arithmetic;
The study of networks that give rise to new mathematical ideas.
The future will undoubtedly be the link between computer science and mathematics in order to consolidate and further strengthen. E 'is now clear that the sisters are in science and its development in the synergistic relationship between them is deep and intense.